Let \(S_A\)  be the reciprocal sum of the sequence \(A\) ; that is,
\(S_A= \sum _{i=1}^\infty \frac{1}{a_i}\) . It is an open problem to find, if it exists, a Sidon sequence \(U\)  whose reciprocal sum is equal to the DDC [1]}. We only know from Taylor and Yovanof [2]} that, if some Sidon sequence achieves the DDC, then it must begin with the values 1, 2, 4.
